Emily wants to determine the relationship between the number of people in a household (x) and the last 4 digits of their phone number (y). She randomly selects 100 households in her town and examines the data.

Question

What is the ,begin emphasis,best,end emphasis, estimate of the correlation coefficient between x and y?

Answer 1

To determine the correlation between the number of people in a household (x) and the last 4 digits of their phone number (y), we need to consider the nature of the two variables.

1. The last 4 digits of a phone number are typically random and do not have any inherent relationship with the number of people in a household.
2. The values of these digits can range from 0000 to 9999, which doesn't correlate systematically with household size.

Given that y (last 4 digits of the phone number) is essentially random with respect to x (household size), the correlation coefficient (r) would be expected to be very close to 0.

Thus, the best estimate of the correlation coefficient between x and y would be 0. This indicates no linear relationship between the number of people in a household and the last 4 digits of their phone number.